The relation between sample and population characteristic vectors

Data are reported which show the statistical relation between the sample and population characteristic vectors of correlation matrices with squared multiple correlations as communality estimates. Sampling fluctuations were found to relate only to differences in the square roots of characteristic roots and to sample size. A principle for determining the number of factors to rotate and interpret after rotation is suggested.This study was supported by the National Science Foundation, Grant GB 4230. The author wishes to express his appreciation for the use of Western Data Processing Center and the Health Sciences Computing Facility, UCLA. He also thanks Dr. Roger Pennell for extremely valuable assistance in a number of phases of the study.